If the walk-outs go ahead as planned on 5 and 6 August, Unite said close to 2,500 staff will miss their shifts.
Heathrow said passengers should contact their airlines in the first instance to see how they may be affected.
Affected passengers may be offered other flights or refunds by their airline, it added.
The airport said its contingency plans will keep Heathrow open and safe on both strike days, albeit with some disruption.
Heathrow advised passengers to check its website for updates.
Passengers still scheduled to fly on Monday and Tuesday have been warned to arrive at least three hours ahead of long-haul departures, and two hours ahead of short-haul departures, as it may take longer to get through security.
Heathrow said the flight cancellations, which affect 91 airlines including British Airways, were a pre-emptive measure in case a solution is not found.
Talks continue
On Friday night, the airport and Unite were still in Advisory, Conciliation and Arbitration Service (ACAS) negotiations to avert the strike action.
A Heathrow spokesperson said: "As part of our plans, we are working with airlines to proactively consolidate flights and rebook passengers onto alternative services in advance.
"We also advise passengers to contact their airlines for the latest information, as well as follow our Twitter and Facebook accounts for further updates."
Unite regional coordinating officer Wayne King said: "This latest vote for strike action points to growing anger among the airport's workers in a whole range of vital jobs which are essential to the smooth and safe running of Heathrow.
"Airport bosses need to heed this latest strike vote and the overwhelming rejection by our members of the revised pay offer which offers little over and above the original offer of £3.75 extra a day for many workers," Mr King said.